## Abstract

This paper describes a system of interferometric control as applied to the smaller ruling engine of the Mount Wilson Observatory. The usual mechanism intermittently advances the grating carriage with a spacing closely approximating an integral number of fringes of green Hg^{198} light. A Michelson interferometer monitors this motion. The interferometer is modulated by deflecting the compensating plate electromagnetically, thus correcting for barometric pressure changes and also causing the fringe pattern to oscillate with a small amplitude at 60 cps. The oscillating fringe pattern is scanned by a phototube and is reproduced on a monitoring cathode-ray tube; any decentering of the *n*th fringe is detected by synchronous demodulation and is converted to a stored electrical charge. During each spacing operation, a differential correction proportional to the stored error signal is introduced into the mechanism. Corrections average about 1 centifringe (2.5 × 10^{−7} cm). The system is relatively simple and ensures a very high order of precision in spacing, with extremely straight grooves.

© 1962 Optical Society of America

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### Equations (6)

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(1)
$$\begin{array}{l}{\u220a}_{1}=b\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{1},\\ {\u220a}_{2}=b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{2}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{1}\right)+\left(1-\beta \right){\u220a}_{1},\\ {\u220a}_{3}=b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{3}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{2}\right)+\left(1-\beta \right){\u220a}_{2},\\ {\u220a}_{n}=b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-1}\right)+\left(1-\beta \right){\u220a}_{n-1}.\end{array}$$
(2)
$$\begin{array}{r}{\u220a}_{n}=b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-1}\right)+\left(1-\beta \right)b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-1}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-2}\right)\\ +{\left(1-\beta \right)}^{2}b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-2}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-3}\right)\\ +{\left(1-\beta \right)}^{3}b\left(\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-3}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-4}\right)+\dots .\end{array}$$
(3)
$$\begin{array}{l}\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-1}\approx \text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-1}-\text{sin}\phantom{\rule{0.2em}{0ex}}{\theta}_{n-2}\\ \phantom{\rule{1em}{0ex}}\approx 2\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\phantom{\rule{0.2em}{0ex}}\left({\theta}_{n}-{\theta}_{n-1}\right)\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\phantom{\rule{0.2em}{0ex}}\left({\theta}_{n}-{\theta}_{n-1}\right)=\frac{2\pi}{N}\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}{\theta}_{n}.\end{array}$$
(4)
$${\u220a}_{n}=\frac{2\pi b}{N}\phantom{\rule{0.2em}{0ex}}\left(3-3\beta +{\beta}^{2}\right)\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}{\theta}_{n}.$$
(5)
$${\u220a}_{n}=2.8\phantom{\rule{0.2em}{0ex}}\frac{\pi b}{N}\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}{\theta}_{n},$$
(6)
$${\u220a}_{n}=0.01\phantom{\rule{0.2em}{0ex}}b\phantom{\rule{0.2em}{0ex}}\text{cos}\phantom{\rule{0.2em}{0ex}}{\theta}_{n}.$$